Q. 10

Mark the correct alternative in each of the following:

The solution of the differential equation represents a circle when

A. a = b

B. a = –b

C. a = –2b

D. a = 2b

Answer :


By Variable separable,


(by + f) dy = (ax + g) dx


Integrating both sides


∫ (by + f) dy = ∫ (ax + g) dx



by2 + 2fy = ax2 + 2gx + C


Where C’ = 2C


We know general solution of circle is


(x – h)2 + (y – k)2 = r2


Where (h, k) is center of the circle and r is radius.


By completing square method





Now to form above equation as equation of circle we need



i.e. a = -b


= (B)

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